Before any such acquisition, eBay (especially) or not, one should contact the seller and ask for a letter of provenance. If they can not or will not provide one, pass on the item. If the provenance is incomplete or suspect, pass on the item. That letter is critical to prove its authenticity and its value. When you have an authentic item, you hold something that the man held, and it doesn't matter how much you paid (at least for us Tolkien enthusiasts). When you buy a fake, it doesn't matter how little you paid for it. So be cautious and take your time. There will "always" be another such item to consider purchasing.

Here is my experience with a signed item:

I acquired a 1974 calendar signed by the professor. I know, "He passed away in September 1973". However, the calendar was issued in August 1973. I asked for and received a detailed explanation before the auction and a personalized and absolutely wonderful letter from the seller after. You may read it and check out his signature (and a short inscription) on my website: